A B C E(r) 8% 10% 9% σ 2 3 1 (i) Is there any security surely NOT chosen by a risk-averse investor? Why? (ii) Suppose the government bans the trading of security C, so the market has only two securities A and B. There are two risk-averse investors, Miss Red and Miss Gray. Miss Red is more risk-averse than Miss Gray. Denote Miss Red’s optimal portfolio choice by PR = ωR ◦ A + (1 − ωR) ◦ B, and Miss Gray’s optimal portfolio choice by PG = ωG ◦ A + (1 − ωG) ◦ B. (a) Without risk-free assets, which one is greater, ωR or ωG? Why? Hint: You don’t need to calculate ωR or ωG to answer this question. (b) Suppose there is a risk-free asset with the rate of return rf = 6%. Both Miss Red and Miss Gray can use the risk-free asset and a risky portfolio to form a new optimal portfolio. The optimal risky portfolios for Miss Red and Miss Gray are denoted by PR and PG, respectively. Then, which one is greater, ωR or ωG? Why? Hint: You don’t need to calculate ωR or ωG to answer this question.
| A | B | C | |
| E(r) | 8% | 10% | 9% |
| σ | 2 | 3 | 1 |
(i) Is there any security surely NOT chosen by a risk-averse investor? Why?
(ii) Suppose the government bans the trading of security C, so the market has only two securities A and B. There are two risk-averse investors, Miss Red and Miss Gray. Miss Red is more risk-averse than Miss Gray. Denote Miss Red’s optimal portfolio choice by PR = ωR ◦ A + (1 − ωR) ◦ B, and Miss Gray’s optimal portfolio choice by PG = ωG ◦ A + (1 − ωG) ◦ B.
(a) Without risk-free assets, which one is greater, ωR or ωG? Why? Hint: You don’t need to calculate ωR or ωG to answer this question.
(b) Suppose there is a risk-free asset with the rate of return rf = 6%. Both Miss Red and Miss Gray can use the risk-free asset and a risky portfolio to form a new optimal portfolio. The optimal risky portfolios for Miss Red and Miss Gray are denoted by PR and PG, respectively. Then, which one is greater, ωR or ωG? Why? Hint: You don’t need to calculate ωR or ωG to answer this question.
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